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Mirrors > Home > ILE Home > Th. List > 0ss | Unicode version |
Description: The null set is a subset of any class. Part of Exercise 1 of [TakeutiZaring] p. 22. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
0ss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3418 | . . 3 | |
2 | 1 | pm2.21i 641 | . 2 |
3 | 2 | ssriv 3151 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2141 wss 3121 c0 3414 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-dif 3123 df-in 3127 df-ss 3134 df-nul 3415 |
This theorem is referenced by: ss0b 3453 ssdifeq0 3496 sssnr 3738 ssprr 3741 uni0 3821 int0el 3859 0disj 3984 disjx0 3986 tr0 4096 0elpw 4148 exmidsssn 4186 fr0 4334 elomssom 4587 rel0 4734 0ima 4969 fun0 5254 f0 5386 el2oss1o 6419 oaword1 6447 0domg 6811 nnnninf 7098 exmidfodomrlemim 7165 pw1on 7190 sum0 11338 prod0 11535 ennnfonelemj0 12343 ennnfonelemkh 12354 0opn 12757 baspartn 12801 0cld 12865 ntr0 12887 bdeq0 13862 bj-omtrans 13951 nninfsellemsuc 14005 |
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